Solve for ‘x’
i) log₃ x = - 2
=> x = 3ˉ²
1 1
=> x = ------- = ------- (Ans.)
3² 9
2
ii) log₂₇ x = --------
3
=> x = (27)⅔ = (3ᶾ)⅔ = 3² = 9 (Ans.)
iii) log √₃ (x + 1) = 2
=> (√3)² = x + 1
=> 3 = x + 1
=> x = 3 – 1
=> x = 2 (Ans.)
iv) log₅ (x² + 9) = 2
=> x² + 9 = 5²
=> x² = 25 – 9
=> x² = 16 = 4²
=> x = ± 4 (Ans.)
3 1
v) logₓ (------) = - -------
4 3
3
=> xˉ⅓ = -------
4
64
=> x⅓ = (-------)⅓
27
64
=> x = -------- (Ans.)
27
vi) log₅ 625 = 2x + 3
=> 5²ˣ⁺³ = 625
=> 5²ˣ⁺³ = 5⁴
=> 2x + 3 = 4
=> 2x = 4 – 3
=> x = 1/2 (Ans.)